Variability analysis

You can study the effect of variability on device performance using the same methods to iterate component parameters to build models.

Lithographic parameters

Not all variability can be captured by simply changing the Component or LayerStack input parameters.

LithoParameter parameters have a parametrizable transformation attribute that you can use to modify the Component geometry prior to simulation in more complex ways than simply changing its calling arguments. The parameter has methods that return a temporary component given an initial component and a transformation type.

Here are the transformations we support so far:

1. Dilation and erosion

2. Corner rounding

3. Offsets

4. Corner rounding

5. Corner analysis

import gdsfactory as gf

c = gf.Component("myComponent")
poly1a = c.add_polygon(
    [
        [2.8,3],
        [5,3],
        [5,0.8]
    ],
    layer="WG",
)
poly1b = c.add_polygon(
    [
        [2, 0],
        [2, 2],
        [4, 2],
        [4, 0],
    ],
    layer="WG",
)
poly1c = c.add_polygon(
    [
        [0, 0.5],
        [0, 1.5],
        [3, 1.5],
        [3, 0.5],
    ],
    layer="WG",
)
poly2 = c.add_polygon(
    [
        [0, 0],
        [5, 0],
        [5, 3],
        [0, 3],
    ],
    layer="SLAB90",
)
poly3 = c.add_polygon(
    [
        [2.5, -2],
        [3.5, -2],
        [3.5, -0.1],
        [2.5, -0.1],
    ],
    layer="WG",
)
c.add_port(name="o1", center=(0,1), width=1, orientation=0, layer=1)
c.add_port(name="o2", center=(3,-2), width=1, orientation=90, layer=1)
c

2023-02-20 17:58:41.871 | INFO     | gdsfactory.config:<module>:50 - Load '/home/runner/work/gdsfactory/gdsfactory/gdsfactory' 6.43.1
2023-02-20 17:58:42.624 | WARNING  | gdsfactory.pdk:get_active_pdk:556 - No active PDK.
Activating the generic PDK
import gdsfactory as gf
PDK = gf.get_generic_pdk()
PDK.activate()
2023-02-20 17:58:42.731 | INFO     | gdsfactory.technology.layer_views:__init__:785 - Importing LayerViews from YAML file: /home/runner/work/gdsfactory/gdsfactory/gdsfactory/generic_tech/layer_views.yaml.
2023-02-20 17:58:42.738 | INFO     | gdsfactory.pdk:activate:206 - 'generic' PDK is now active

myComponent: uid 46d18b80, ports ['o1', 'o2'], references [], 5 polygons

Dilation and erosion

A LithoParameter of type = "layer_dilation_erosion" parametrizes a layerwise growing (positive value) or shrinking (negative value) of the geometry. Note that the ports are properly resized when they are on the transformed layer:

from gdsfactory.simulation.sax.parameter import LithoParameter

param = LithoParameter(layername="core")
eroded_c = param.layer_dilation_erosion(c, 0.2)
eroded_c

/home/runner/work/gdsfactory/gdsfactory/gdsfactory/component.py:1684: UserWarning: Component 'Unnamed_a2916ba2' contains 1 Unnamed cells
  warnings.warn(

Unnamed_a2916ba2: uid a2916ba2, ports ['o1', 'o2'], references [], 3 polygons

param = LithoParameter(layername="core")
eroded_c = param.layer_dilation_erosion(c, -0.3)
eroded_c

/home/runner/work/gdsfactory/gdsfactory/gdsfactory/component.py:1684: UserWarning: Component 'Unnamed_996ac54a' contains 1 Unnamed cells
  warnings.warn(

Unnamed_996ac54a: uid 996ac54a, ports ['o1', 'o2'], references [], 4 polygons

param = LithoParameter(layername="slab90")
eroded_c = param.layer_dilation_erosion(c, 0.2)
eroded_c

/home/runner/work/gdsfactory/gdsfactory/gdsfactory/component.py:1684: UserWarning: Component 'Unnamed_6d3e9d9d' contains 1 Unnamed cells
  warnings.warn(

Unnamed_6d3e9d9d: uid 6d3e9d9d, ports ['o1', 'o2'], references [], 5 polygons

Offsets

Lithography can sometimes laterally offset layers w.r.t. to one another. This is captured by layerwise type = "layer_x_offset" and type = "layer_x_offset". Note that ports are also translated:

param = LithoParameter(layername="core")
offset_c = param.layer_x_offset(c, 0.5)
offset_c

/home/runner/work/gdsfactory/gdsfactory/gdsfactory/component.py:1684: UserWarning: Component 'Unnamed_15217f6a' contains 1 Unnamed cells
  warnings.warn(

Unnamed_15217f6a: uid 15217f6a, ports ['o1', 'o2'], references [], 5 polygons

param = LithoParameter(layername="core")
offset_c = param.layer_y_offset(c, -0.5)
offset_c

/home/runner/work/gdsfactory/gdsfactory/gdsfactory/component.py:1684: UserWarning: Component 'Unnamed_2e533a9a' contains 1 Unnamed cells
  warnings.warn(

Unnamed_2e533a9a: uid 2e533a9a, ports ['o1', 'o2'], references [], 5 polygons

Corner rounding

The erosion and dilation above is done with “worst case” sharp corners. An erosion –> dilation –> erosion sequence, accessible with type = "layer_round_corners" can be done to parametrize corner rounding. For ports, here parts of the geometry overlapping with ports are patched to prevent the ports from being off the layer.

param = LithoParameter(layername="core")
smooth_c = param.layer_round_corners(c, 0.1)
smooth_c

/home/runner/work/gdsfactory/gdsfactory/gdsfactory/component.py:1684: UserWarning: Component 'Unnamed_bd0bd413' contains 1 Unnamed cells
  warnings.warn(

Unnamed_bd0bd413: uid bd0bd413, ports ['o1', 'o2'], references ['extrude_1', 'extrude_2'], 3 polygons

param = LithoParameter(layername="core")
smooth_c = param.layer_round_corners(c, 0.4)
smooth_c

/home/runner/work/gdsfactory/gdsfactory/gdsfactory/component.py:1684: UserWarning: Component 'Unnamed_9f4ed8e2' contains 1 Unnamed cells
  warnings.warn(

Unnamed_9f4ed8e2: uid 9f4ed8e2, ports ['o1', 'o2'], references ['extrude_1', 'extrude_2'], 3 polygons

Corner analysis

For convenience, the model builder can also iterate over only the min, max, and nominal values of all trainable_parameters by using the types=corners instead of the default types=arange argument of Model.get_model_input_output(type="corners").

Directional coupler example

Consider a directional coupler component which is modeled through a generic MeepFDTDModel. The only difference between this and the FemwellWaveguideModel from last notebook is how the simulation is defined: everything else involving iteration over parameters, multiprocessing, and model fitting, is identical. This makes model building easily extensible to new simulators.

Here, we are only interested in variability analysis of the geometry, and so we create a trainable coupler with fixed length and gap:

import gdsfactory as gf
from gdsfactory.simulation.sax.parameter import NamedParameter
from gdsfactory.technology import LayerStack
from gdsfactory.pdk import _ACTIVE_PDK, get_layer_stack


# gdsfactory layerstack
filtered_layerstack = LayerStack(
    layers={
        k: get_layer_stack().layers[k]
        for k in (
            "slab90",
            "core",
            "box",
            "clad",
        )
    }
)

# trainable component function, choosing which parameters to fix and which to consider for the model
def trainable_coupler(parameters):
    return gf.components.coupler_full(
        coupling_length=10,
        gap=0.3,
        dw=0.0,
    )

c = trainable_coupler({})
c

coupler_full_22f3e7c9: uid 9c590480, ports ['o1', 'o2', 'o3', 'o4'], references [], 6 polygons

When defining the model, we add the LithoParameter erosion_magnitude. For all models, a TransformParameter which if set, will offset the provided component prior to simulation, emulating erosion (when <1), nominal behaviour (when 1) and dilation (when >1). This morphological transformation is currently global; more advanced spatially-correlated filters are an obvious next step.

from gdsfactory.simulation.sax.meep_FDTD_model import MeepFDTDModel

# Simulation settings
port_symmetries_coupler = {
    "o1@0,o1@0": ["o2@0,o2@0", "o3@0,o3@0", "o4@0,o4@0"],
    "o2@0,o1@0": ["o1@0,o2@0", "o3@0,o4@0", "o4@0,o3@0"],
    "o3@0,o1@0": ["o1@0,o3@0", "o2@0,o4@0", "o4@0,o2@0"],
    "o4@0,o1@0": ["o1@0,o4@0", "o2@0,o3@0", "o3@0,o2@0"],
}

sim_settings = dict(
    resolution=30,
    xmargin=1.0,
    ymargin=1.0,
    is_3d=False,
    port_source_names=["o1"],
    port_symmetries=port_symmetries_coupler,
    run=True,
    overwrite=False,
    layer_stack=filtered_layerstack,
    z=0.1,
)


coupler_model = MeepFDTDModel(trainable_component=trainable_coupler,
    layerstack=filtered_layerstack,
    simulation_settings={
        "sim_settings": sim_settings,
    },
    trainable_parameters={
        "dilation_magnitude": LithoParameter(
            type="layer_dilation_erosion", layername="core", min_value=-0.05, max_value=0.05, nominal_value=0.0, step=0.05
        ),
    },
    non_trainable_parameters={
        "wavelength": NamedParameter(
            min_value=1.54, max_value=1.56, nominal_value=1.55, step=0.01
        ),
    },
    num_modes=1,
)

2023-02-20 17:58:50.025 | INFO     | gdsfactory.simulation.gmeep:<module>:34 - Meep '1.25.0-beta' installed at ['/usr/share/miniconda/envs/anaconda-client-env/lib/python3.9/site-packages/meep']

Using MPI version 4.0, 1 processes

# input_vectors, output_vectors = coupler_model.get_model_input_output(type="corners")

We can analyze the output vectors as a function of input vectors to study variability (TODO).

Since such a change of morphology can also be approximated with a change in gap and waveguide width of the original component, we can compare the results to a model of the component with these as swept NamedParameters (TODO).